Twinning by syngonic and metric merohedry. Analysis, classification and effects on the diffraction pattern

Abstract

Twinning by merohedry involves crystals whose point group is a subgroup of the lattice symmetry. The case of crystals with a metric symmetry higher than the syngony, not considered in the previous classifications of twinning, is here analysed in terms of group-subgroup relations and pseudo-symmetry. Merohedry is classified into syngonic merohedry and metric merohedry, depending on whether the crystal lattice symmetry is equal to or higher than the syngony. It is shown that the metric merohedry corresponds to the degeneration of the pseudo-merohedry to zero obliquity, or to the degeneration of the reticular merohedry to twin index 1. A revised classification of merohedry into three classes, on the basis of the symmetry of the twin, is given. Class I includes twins in which the twin operation belongs to the Laue point group of the individual. Class IIA includes twins in which the twin operation belongs to the syngony of the individual but not to its Laue point group. Finally class IIB includes twins in which the twin operation does not belong to the syngony of the individual. The effect of the classes of twins onto the diffraction pattern is discussed.